English

Special birational transformations of projective spaces

Algebraic Geometry 2013-09-13 v2

Abstract

Extending some results of Crauder and Katz, and Ein and Shepherd-Barron on special Cremona transformations, we study birational transformations of the complex projective spaces onto prime Fano manifolds such that the base locus X of the transformations is smooth, irreducible and reduced. We get a complete classification when X has dimension 1, or dimension 2, or codimension 2. We also get partial results when X has dimension 3.

Keywords

Cite

@article{arxiv.1203.5690,
  title  = {Special birational transformations of projective spaces},
  author = {Alberto Alzati and José Carlos Sierra},
  journal= {arXiv preprint arXiv:1203.5690},
  year   = {2013}
}

Comments

Minor mistake in Theorem 7 corrected, references updated

R2 v1 2026-06-21T20:39:55.577Z